{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cruise control\n",
    "\n",
    "Richard M. Murray and Karl J. Åström  \n",
    "17 Jun 2019\n",
    "\n",
    "The cruise control system of a car is a common feedback system encountered in everyday life. The system attempts to maintain a constant velocity in the presence of disturbances primarily caused by changes in the slope of a road. The controller compensates for these unknowns by measuring the speed of the car and adjusting the throttle appropriately.\n",
    "\n",
    "This notebook explores the dynamics and control of the cruise control system, following the material presenting in Feedback Systems by Astrom and Murray.  A nonlinear model of the vehicle dynamics is used, with both state space and frequency domain control laws.  The process model is presented in Section 1, and a controller based on state feedback is discussed in Section 2, where we also add integral action to the controller. In Section 3 we explore the behavior with PI control including the effect of actuator saturation and how it is avoided by windup protection.  Different methods of constructing control systems are shown, all using the InputOutputSystem class (and subclasses)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import pi\n",
    "import control as ct"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process Model\n",
    "\n",
    "### Vehicle Dynamics\n",
    "\n",
    "To develop a mathematical model we start with a force balance for the car body. Let $v$ be the speed of the car, $m$ the total mass (including passengers), $F$ the force generated by the contact of the wheels with the road, and $F_d$ the disturbance force due to gravity, friction, and aerodynamic drag."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vehicle_update(t, x, u, params={}):\n",
    "    \"\"\"Vehicle dynamics for cruise control system.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x : array\n",
    "         System state: car velocity in m/s\n",
    "    u : array\n",
    "         System input: [throttle, gear, road_slope], where throttle is\n",
    "         a float between 0 and 1, gear is an integer between 1 and 5,\n",
    "         and road_slope is in rad.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float\n",
    "        Vehicle acceleration\n",
    "\n",
    "    \"\"\"\n",
    "    from math import copysign, sin\n",
    "    sign = lambda x: copysign(1, x)         # define the sign() function\n",
    "    \n",
    "    # Set up the system parameters\n",
    "    m = params.get('m', 1600.)              # vehicle mass, kg\n",
    "    g = params.get('g', 9.8)                # gravitational constant, m/s^2\n",
    "    Cr = params.get('Cr', 0.01)             # coefficient of rolling friction\n",
    "    Cd = params.get('Cd', 0.32)             # drag coefficient\n",
    "    rho = params.get('rho', 1.3)            # density of air, kg/m^3\n",
    "    A = params.get('A', 2.4)                # car area, m^2\n",
    "    alpha = params.get(\n",
    "        'alpha', [40, 25, 16, 12, 10])      # gear ratio / wheel radius\n",
    "\n",
    "    # Define variables for vehicle state and inputs\n",
    "    v = x[0]                           # vehicle velocity\n",
    "    throttle = np.clip(u[0], 0, 1)     # vehicle throttle\n",
    "    gear = u[1]                        # vehicle gear\n",
    "    theta = u[2]                       # road slope\n",
    "\n",
    "    # Force generated by the engine\n",
    "\n",
    "    omega = alpha[int(gear)-1] * v      # engine angular speed\n",
    "    F = alpha[int(gear)-1] * motor_torque(omega, params) * throttle\n",
    "\n",
    "    # Disturbance forces\n",
    "    #\n",
    "    # The disturbance force Fd has three major components: Fg, the forces due\n",
    "    # to gravity; Fr, the forces due to rolling friction; and Fa, the\n",
    "    # aerodynamic drag.\n",
    "\n",
    "    # Letting the slope of the road be \\theta (theta), gravity gives the\n",
    "    # force Fg = m g sin \\theta.\n",
    "    \n",
    "    Fg = m * g * sin(theta)\n",
    "\n",
    "    # A simple model of rolling friction is Fr = m g Cr sgn(v), where Cr is\n",
    "    # the coefficient of rolling friction and sgn(v) is the sign of v (±1) or\n",
    "    # zero if v = 0.\n",
    "    \n",
    "    Fr  = m * g * Cr * sign(v)\n",
    "\n",
    "    # The aerodynamic drag is proportional to the square of the speed: Fa =\n",
    "    # 1/2 \\rho Cd A |v| v, where \\rho is the density of air, Cd is the\n",
    "    # shape-dependent aerodynamic drag coefficient, and A is the frontal area\n",
    "    # of the car.\n",
    "\n",
    "    Fa = 1/2 * rho * Cd * A * abs(v) * v\n",
    "    \n",
    "    # Final acceleration on the car\n",
    "    Fd = Fg + Fr + Fa\n",
    "    dv = (F - Fd) / m\n",
    "    \n",
    "    return dv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Engine model\n",
    "\n",
    "The force F is generated by the engine, whose torque is proportional to the rate of fuel injection, which is itself proportional to a control signal 0 <= u <= 1 that controls the throttle position. The torque also depends on engine speed omega."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def motor_torque(omega, params={}):\n",
    "    # Set up the system parameters\n",
    "    Tm = params.get('Tm', 190.)             # engine torque constant\n",
    "    omega_m = params.get('omega_m', 420.)   # peak engine angular speed\n",
    "    beta = params.get('beta', 0.4)          # peak engine rolloff\n",
    "\n",
    "    return np.clip(Tm * (1 - beta * (omega/omega_m - 1)**2), 0, None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Torque curves for a typical car engine. The graph on the left shows the torque generated by the engine as a function of the angular velocity of the engine, while the curve on the right shows torque as a function of car speed for different gears."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figure 4.2\n",
    "fig, axes = plt.subplots(1, 2, figsize=(7, 3))\n",
    "\n",
    "# (a) - single torque curve as function of omega\n",
    "ax = axes[0]\n",
    "omega = np.linspace(0, 700, 701)\n",
    "ax.plot(omega, motor_torque(omega))\n",
    "ax.set_xlabel(r'Angular velocity $\\omega$ [rad/s]')\n",
    "ax.set_ylabel('Torque $T$ [Nm]')\n",
    "ax.grid(True, linestyle='dotted')\n",
    "\n",
    "# (b) - torque curves in different gears, as function of velocity\n",
    "ax = axes[1]\n",
    "v = np.linspace(0, 70, 71)\n",
    "alpha = [40, 25, 16, 12, 10]\n",
    "for gear in range(5):\n",
    "    omega = alpha[gear] * v\n",
    "    T = motor_torque(omega)\n",
    "    plt.plot(v, T, color='#1f77b4', linestyle='solid')\n",
    "\n",
    "# Set up the axes and style\n",
    "ax.axis([0, 70, 100, 200])\n",
    "ax.grid(True, linestyle='dotted')\n",
    "\n",
    "# Add labels\n",
    "plt.text(11.5, 120, '$n$=1')\n",
    "ax.text(24, 120, '$n$=2')\n",
    "ax.text(42.5, 120, '$n$=3')\n",
    "ax.text(58.5, 120, '$n$=4')\n",
    "ax.text(58.5, 185, '$n$=5')\n",
    "ax.set_xlabel('Velocity $v$ [m/s]')\n",
    "ax.set_ylabel('Torque $T$ [Nm]')\n",
    "\n",
    "plt.suptitle('Torque curves for typical car engine')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input/ouput model for the vehicle system\n",
    "\n",
    "We now create an input/output model for the vehicle system that takes the throttle input $u$, the gear and the angle of the road $\\theta$ as input.  The output of this model is the current vehicle velocity $v$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "vehicle = ct.NonlinearIOSystem(\n",
    "    vehicle_update, None, name='vehicle',\n",
    "    inputs = ('u', 'gear', 'theta'), outputs = ('v'), states=('v'))\n",
    "\n",
    "# Define a function for creating a \"standard\" cruise control plot\n",
    "def cruise_plot(sys, t, y, label=None, t_hill=None, vref=20, antiwindup=False,\n",
    "                linetype='b-', subplots=None, legend=None):\n",
    "    if subplots is None:\n",
    "        subplots = [None, None]\n",
    "    # Figure out the plot bounds and indices\n",
    "    v_min = vref - 1.2; v_max = vref + 0.5; v_ind = sys.find_output('v')\n",
    "    u_min = 0; u_max = 2 if antiwindup else 1; u_ind = sys.find_output('u')\n",
    "\n",
    "    # Make sure the upper and lower bounds on v are OK\n",
    "    while max(y[v_ind]) > v_max: v_max += 1\n",
    "    while min(y[v_ind]) < v_min: v_min -= 1\n",
    "\n",
    "    # Create arrays for return values\n",
    "    subplot_axes = list(subplots)\n",
    "\n",
    "    # Velocity profile\n",
    "    if subplot_axes[0] is None:\n",
    "        subplot_axes[0] = plt.subplot(2, 1, 1)\n",
    "    else:\n",
    "        plt.sca(subplots[0])\n",
    "    plt.plot(t, y[v_ind], linetype)\n",
    "    plt.plot(t, vref*np.ones(t.shape), 'k-')\n",
    "    if t_hill:\n",
    "        plt.axvline(t_hill, color='k', linestyle='--', label='t hill')\n",
    "    plt.axis([0, t[-1], v_min, v_max])\n",
    "    plt.xlabel('Time $t$ [s]')\n",
    "    plt.ylabel('Velocity $v$ [m/s]')\n",
    "\n",
    "    # Commanded input profile\n",
    "    if subplot_axes[1] is None:\n",
    "        subplot_axes[1] = plt.subplot(2, 1, 2)\n",
    "    else:\n",
    "        plt.sca(subplots[1])\n",
    "    plt.plot(t, y[u_ind], 'r--' if antiwindup else linetype, label=label)\n",
    "    # Applied input profile\n",
    "    if antiwindup:\n",
    "        plt.plot(t, np.clip(y[u_ind], 0, 1), linetype, label='Applied')\n",
    "    if t_hill:\n",
    "        plt.axvline(t_hill, color='k', linestyle='--')\n",
    "    if legend:\n",
    "        plt.legend(frameon=False)\n",
    "    plt.axis([0, t[-1], u_min, u_max])\n",
    "    plt.xlabel('Time $t$ [s]')\n",
    "    plt.ylabel('Throttle $u$')\n",
    "\n",
    "    return subplot_axes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State space controller\n",
    "\n",
    "Construct a state space controller with integral action, linearized around an equilibrium point.  The controller is constructed around the equilibrium point $(x_d, u_d)$ and includes both feedforward and feedback compensation.\n",
    "\n",
    "* Controller inputs - $(x, y, r)$: system states, system output, reference\n",
    "* Controller state - $z$: integrated error $(y - r)$\n",
    "* Controller output - $u$: state feedback control\n",
    "\n",
    "Note: to make the structure of the controller more clear, we implement this as a \"nonlinear\" input/output module, even though the actual input/output system is linear.  This also allows the use of parameters to set the operating point and gains for the controller.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Xeq =  [20.]\n",
      "Ueq =  [0.16874874 4.         0.        ]\n"
     ]
    }
   ],
   "source": [
    "def sf_update(t, z, u, params={}):\n",
    "    y, r = u[1], u[2]\n",
    "    return y - r\n",
    "\n",
    "def sf_output(t, z, u, params={}):\n",
    "    # Get the controller parameters that we need\n",
    "    K = params.get('K', 0)\n",
    "    ki = params.get('ki', 0)\n",
    "    kf = params.get('kf', 0)\n",
    "    xd = params.get('xd', 0)\n",
    "    yd = params.get('yd', 0)\n",
    "    ud = params.get('ud', 0)\n",
    "\n",
    "    # Get the system state and reference input\n",
    "    x, y, r = u[0], u[1], u[2]\n",
    "\n",
    "    return ud - K * (x - xd) - ki * z + kf * (r - yd)\n",
    "\n",
    "# Create the input/output system for the controller\n",
    "control_sf = ct.NonlinearIOSystem(\n",
    "    sf_update, sf_output, name='control',\n",
    "    inputs=('x', 'y', 'r'),\n",
    "    outputs=('u'),\n",
    "    states=('z'))\n",
    "\n",
    "# Create the closed loop system for the state space controller\n",
    "cruise_sf = ct.InterconnectedSystem(\n",
    "    [vehicle, control_sf], name='cruise',\n",
    "    connections=[\n",
    "        ['vehicle.u', 'control.u'],\n",
    "        ['control.x', 'vehicle.v'],\n",
    "        ['control.y', 'vehicle.v']],\n",
    "    inplist=['control.r', 'vehicle.gear', 'vehicle.theta'],\n",
    "    outlist=['control.u', 'vehicle.v'], outputs=['u', 'v'])\n",
    "\n",
    "# Define the time and input vectors\n",
    "T = np.linspace(0, 25, 501)\n",
    "vref = 20 * np.ones(T.shape)\n",
    "gear = 4 * np.ones(T.shape)\n",
    "theta0 = np.zeros(T.shape)\n",
    "\n",
    "# Find the equilibrium point for the system\n",
    "Xeq, Ueq = ct.find_eqpt(\n",
    "    vehicle, [vref[0]], [0, gear[0], theta0[0]], y0=[vref[0]], iu=[1, 2])\n",
    "print(\"Xeq = \", Xeq)\n",
    "print(\"Ueq = \", Ueq)\n",
    "\n",
    "# Compute the linearized system at the eq pt\n",
    "cruise_linearized = ct.linearize(vehicle, Xeq, [Ueq[0], gear[0], 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Construct the gain matrices for the system\n",
    "A, B, C = cruise_linearized.A, cruise_linearized.B[0, 0], cruise_linearized.C\n",
    "K = 0.5\n",
    "kf = -1 / (C * np.linalg.inv(A - B * K) * B)\n",
    "\n",
    "# Compute the steady state velocity and throttle setting\n",
    "xd = Xeq[0]\n",
    "ud = Ueq[0]\n",
    "yd = vref[-1]\n",
    "\n",
    "# Response of the system with no integral feedback term\n",
    "plt.figure()\n",
    "theta_hill = [\n",
    "    0 if t <= 5 else\n",
    "    4./180. * pi * (t-5) if t <= 6 else\n",
    "    4./180. * pi for t in T]\n",
    "t, y_sfb = ct.input_output_response(\n",
    "    cruise_sf, T, [vref, gear, theta_hill], [Xeq[0], 0],\n",
    "    params={'K':K, 'ki':0.0, 'kf':kf, 'xd':xd, 'ud':ud, 'yd':yd})\n",
    "subplots = cruise_plot(cruise_sf, t, y_sfb, t_hill=5, linetype='b--')\n",
    "\n",
    "# Response of the system with state feedback + integral action\n",
    "t, y_sfb_int = ct.input_output_response(\n",
    "    cruise_sf, T, [vref, gear, theta_hill], [Xeq[0], 0],\n",
    "    params={'K':K, 'ki':0.1, 'kf':kf, 'xd':xd, 'ud':ud, 'yd':yd})\n",
    "cruise_plot(cruise_sf, t, y_sfb_int, t_hill=5, linetype='b-', subplots=subplots)\n",
    "\n",
    "# Add title and legend\n",
    "plt.suptitle('Cruise control with state feedback, integral action')\n",
    "import matplotlib.lines as mlines\n",
    "p_line = mlines.Line2D([], [], color='blue', linestyle='--', label='State feedback')\n",
    "pi_line = mlines.Line2D([], [], color='blue', linestyle='-', label='w/ integral action')\n",
    "plt.legend(handles=[p_line, pi_line], frameon=False, loc='lower right');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pole/zero cancellation\n",
    "\n",
    "The transfer function for the linearized dynamics of the cruise control system is given by $P(s) = b/(s+a)$.  A simple (but not necessarily good) way to design a PI controller is to choose the parameters of the PI controller as $k_\\text{i}=ak_\\text{p}$.  The controller transfer function is then $C(s)=k_\\text{p}+k_\\text{i}/s=k_\\text{i}(s+a)/s$. It has a zero at $s = -k_\\text{i}/k_\\text{p}=-a$ that cancels the process pole at $s = -a$. We have $P(s)C(s)=k_\\text{i}/s$ giving the transfer function from reference to vehicle velocity as $G_{yr}(s)=b k_\\text{p}/(s + b k_\\text{p})$, and control design is then simply a matter of choosing the gain $k_\\text{p}$. The closed loop system dynamics are of first order with the time constant $1/(b k_\\text{p})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "system: a =  0.010124405669387215 , b =  1.3203061238159202\n",
      "pzcancel: kp = 0.5 , ki = 0.005062202834693608 , 1/(kp b) =  1.5148002148317266\n",
      "sfb_int: K =  0.5 , ki = 0.1\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the transfer function from throttle input + hill to vehicle speed\n",
    "P = ct.ss2tf(cruise_linearized[0, 0])\n",
    "\n",
    "# Construction a controller that cancels the pole\n",
    "kp = 0.5\n",
    "a = -P.poles()[0].real\n",
    "b = np.real(P(0)) * a\n",
    "ki = a * kp\n",
    "control_pz = ct.TransferFunction(\n",
    "    [kp, ki], [1, 0], name='control', inputs='u', outputs='y')\n",
    "print(\"system: a = \", a, \", b = \", b)\n",
    "print(\"pzcancel: kp =\", kp, \", ki =\", ki, \", 1/(kp b) = \", 1/(kp * b))\n",
    "print(\"sfb_int: K = \", K, \", ki = 0.1\")\n",
    "\n",
    "# Construct the closed loop system and plot the response\n",
    "# Create the closed loop system for the state space controller\n",
    "cruise_pz = ct.InterconnectedSystem(\n",
    "    [vehicle, control_pz], name='cruise_pz',\n",
    "    connections = [\n",
    "        ['control.u', '-vehicle.v'],\n",
    "        ['vehicle.u', 'control.y']],\n",
    "    inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'],\n",
    "    inputs = ['vref', 'gear', 'theta'],\n",
    "    outlist = ['vehicle.v', 'vehicle.u'],\n",
    "    outputs = ['v', 'u'])\n",
    "\n",
    "# Find the equilibrium point\n",
    "X0, U0 = ct.find_eqpt(\n",
    "    cruise_pz, [vref[0], 0], [vref[0], gear[0], theta0[0]], \n",
    "    iu=[1, 2], y0=[vref[0], 0], iy=[0])\n",
    "\n",
    "# Response of the system with PI controller canceling process pole\n",
    "t, y_pzcancel = ct.input_output_response(\n",
    "    cruise_pz, T, [vref, gear, theta_hill], X0)\n",
    "subplots = cruise_plot(cruise_pz, t, y_pzcancel, t_hill=5, linetype='b-')\n",
    "cruise_plot(cruise_sf, t, y_sfb_int, t_hill=5, linetype='b--', subplots=subplots);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PI Controller\n",
    "\n",
    "In this example, the speed of the vehicle is measured and compared to the desired speed.  The controller is a PI controller represented as a transfer function.  In the textbook, the simulations are done for LTI systems, but here we simulate the full nonlinear system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameter design through pole placement\n",
    "\n",
    "To illustrate the design of a PI controller, we choose the gains $k_\\text{p}$ and $k_\\text{i}$ so that the characteristic polynomial has the form\n",
    "\n",
    "$$\n",
    "s^2 + 2 \\zeta \\omega_0 s + \\omega_0^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Values of the first order transfer function P(s) = b/(s + a) are set above\n",
    "\n",
    "# Define the input that we want to track\n",
    "T = np.linspace(0, 40, 101)\n",
    "vref = 20 * np.ones(T.shape)\n",
    "gear = 4 * np.ones(T.shape)\n",
    "theta_hill = np.array([\n",
    "    0 if t <= 5 else\n",
    "    4./180. * pi * (t-5) if t <= 6 else\n",
    "    4./180. * pi for t in T])\n",
    "\n",
    "# Fix \\omega_0 and vary \\zeta\n",
    "w0 = 0.5\n",
    "subplots = [None, None]\n",
    "for zeta in [0.5, 1, 2]:\n",
    "    # Create the controller transfer function (as an I/O system)\n",
    "    kp = (2*zeta*w0 - a)/b\n",
    "    ki = w0**2 / b\n",
    "    control_tf = ct.TransferFunction(\n",
    "        [kp, ki], [1, 0.01*ki/kp], name='control', inputs='u', outputs='y')\n",
    "    \n",
    "    # Construct the closed loop system by interconnecting process and controller\n",
    "    cruise_tf = ct.InterconnectedSystem(\n",
    "    [vehicle, control_tf], name='cruise',\n",
    "    connections = [['control.u', '-vehicle.v'], ['vehicle.u', 'control.y']],\n",
    "    inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'], \n",
    "        inputs = ['vref', 'gear', 'theta'],\n",
    "    outlist = ['vehicle.v', 'vehicle.u'], outputs = ['v', 'u'])\n",
    "\n",
    "    # Plot the velocity response\n",
    "    X0, U0 = ct.find_eqpt(\n",
    "        cruise_tf, [vref[0], 0], [vref[0], gear[0], theta_hill[0]], \n",
    "        iu=[1, 2], y0=[vref[0], 0], iy=[0])\n",
    "\n",
    "    t, y = ct.input_output_response(cruise_tf, T, [vref, gear, theta_hill], X0)\n",
    "    subplots = cruise_plot(cruise_tf, t, y, t_hill=5, subplots=subplots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fix \\zeta and vary \\omega_0\n",
    "zeta = 1\n",
    "subplots = [None, None]\n",
    "for w0 in [0.2, 0.5, 1]:\n",
    "    # Create the controller transfer function (as an I/O system)\n",
    "    kp = (2*zeta*w0 - a)/b\n",
    "    ki = w0**2 / b\n",
    "    control_tf = ct.TransferFunction(\n",
    "        [kp, ki], [1, 0.01*ki/kp], name='control', inputs='u', outputs='y')\n",
    "    \n",
    "    # Construct the closed loop system by interconnecting process and controller\n",
    "    cruise_tf = ct.InterconnectedSystem(\n",
    "    [vehicle, control_tf], name='cruise',\n",
    "    connections = [['control.u', '-vehicle.v'], ['vehicle.u', 'control.y']],\n",
    "    inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'], \n",
    "        inputs = ['vref', 'gear', 'theta'],\n",
    "    outlist = ['vehicle.v', 'vehicle.u'], outputs = ['v', 'u'])\n",
    "\n",
    "    # Plot the velocity response\n",
    "    X0, U0 = ct.find_eqpt(\n",
    "        cruise_tf, [vref[0], 0], [vref[0], gear[0], theta_hill[0]], \n",
    "        iu=[1, 2], y0=[vref[0], 0], iy=[0])\n",
    "\n",
    "    t, y = ct.input_output_response(cruise_tf, T, [vref, gear, theta_hill], X0)\n",
    "    subplots = cruise_plot(cruise_tf, t, y, t_hill=5, subplots=subplots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robustness to change in mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Nominal controller design for remaining analyses\n",
    "# Construct a PI controller with rolloff, as a transfer function\n",
    "Kp = 0.5                        # proportional gain\n",
    "Ki = 0.1                        # integral gain\n",
    "control_tf = ct.TransferFunction(\n",
    "    [Kp, Ki], [1, 0.01*Ki/Kp], name='control', inputs='u', outputs='y')\n",
    "\n",
    "cruise_tf = ct.InterconnectedSystem(\n",
    "    [vehicle, control_tf], name='cruise',\n",
    "    connections = [['control.u', '-vehicle.v'], ['vehicle.u', 'control.y']],\n",
    "    inplist = ['control.u', 'vehicle.gear', 'vehicle.theta'], inputs = ['vref', 'gear', 'theta'],\n",
    "    outlist = ['vehicle.v', 'vehicle.u'], outputs = ['v', 'u'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the time and input vectors\n",
    "T = np.linspace(0, 25, 101)\n",
    "vref = 20 * np.ones(T.shape)\n",
    "gear = 4 * np.ones(T.shape)\n",
    "theta0 = np.zeros(T.shape)\n",
    "\n",
    "# Now simulate the effect of a hill at t = 5 seconds\n",
    "plt.figure()\n",
    "plt.suptitle('Response to change in road slope')\n",
    "theta_hill = np.array([\n",
    "    0 if t <= 5 else\n",
    "    4./180. * pi * (t-5) if t <= 6 else\n",
    "    4./180. * pi for t in T])\n",
    "\n",
    "subplots = [None, None]\n",
    "linecolor = ['red', 'blue', 'green']\n",
    "handles = []\n",
    "for i, m in enumerate([1200, 1600, 2000]):\n",
    "    # Compute the equilibrium state for the system\n",
    "    X0, U0 = ct.find_eqpt(\n",
    "        cruise_tf, [vref[0], 0], [vref[0], gear[0], theta0[0]], \n",
    "        iu=[1, 2], y0=[vref[0], 0], iy=[0], params={'m':m})\n",
    "\n",
    "    t, y = ct.input_output_response(\n",
    "        cruise_tf, T, [vref, gear, theta_hill], X0, params={'m':m})\n",
    "\n",
    "    subplots = cruise_plot(cruise_tf, t, y, t_hill=5, subplots=subplots,\n",
    "                           linetype=linecolor[i][0] + '-')\n",
    "    handles.append(mlines.Line2D([], [], color=linecolor[i], linestyle='-', \n",
    "                                 label=\"m = %d\" % m))\n",
    "\n",
    "# Add labels to the plots\n",
    "plt.sca(subplots[0])\n",
    "plt.ylabel('Speed [m/s]')\n",
    "plt.legend(handles=handles, frameon=False, loc='lower right');\n",
    "\n",
    "plt.sca(subplots[1])\n",
    "plt.ylabel('Throttle')\n",
    "plt.xlabel('Time [s]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PI controller with  antiwindup protection\n",
    "\n",
    "We now create a more complicated feedback controller that includes anti-windup protection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pi_update(t, x, u, params={}):\n",
    "    # Get the controller parameters that we need\n",
    "    ki = params.get('ki', 0.1)\n",
    "    kaw = params.get('kaw', 2)  # anti-windup gain\n",
    "\n",
    "    # Assign variables for inputs and states (for readability)\n",
    "    v = u[0]                    # current velocity\n",
    "    vref = u[1]                 # reference velocity\n",
    "    z = x[0]                    # integrated error\n",
    "\n",
    "    # Compute the nominal controller output (needed for anti-windup)\n",
    "    u_a = pi_output(t, x, u, params)\n",
    "\n",
    "    # Compute anti-windup compensation (scale by ki to account for structure)\n",
    "    u_aw = kaw/ki * (np.clip(u_a, 0, 1) - u_a) if ki != 0 else 0\n",
    "\n",
    "    # State is the integrated error, minus anti-windup compensation\n",
    "    return (vref - v) + u_aw\n",
    "\n",
    "def pi_output(t, x, u, params={}):\n",
    "    # Get the controller parameters that we need\n",
    "    kp = params.get('kp', 0.5)\n",
    "    ki = params.get('ki', 0.1)\n",
    "\n",
    "    # Assign variables for inputs and states (for readability)\n",
    "    v = u[0]                    # current velocity\n",
    "    vref = u[1]                 # reference velocity\n",
    "    z = x[0]                    # integrated error\n",
    "\n",
    "    # PI controller\n",
    "    return kp * (vref - v) + ki * z\n",
    "\n",
    "control_pi = ct.NonlinearIOSystem(\n",
    "    pi_update, pi_output, name='control',\n",
    "    inputs = ['v', 'vref'], outputs = ['u'], states = ['z'],\n",
    "    params = {'kp':0.5, 'ki':0.1})\n",
    "\n",
    "# Create the closed loop system\n",
    "cruise_pi = ct.InterconnectedSystem(\n",
    "    [vehicle, control_pi], name='cruise',\n",
    "    connections=[\n",
    "        ['vehicle.u', 'control.u'],\n",
    "        ['control.v', 'vehicle.v']],\n",
    "    inplist=['control.vref', 'vehicle.gear', 'vehicle.theta'],\n",
    "    outlist=['control.u', 'vehicle.v'], outputs=['u', 'v'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Response to a small hill\n",
    "\n",
    "Figure 4.3b shows the response of the closed loop system.  The figure shows that even if the hill is so steep that the throttle changes from 0.17 to almost full throttle, the largest speed error is less than 1 m/s, and the desired velocity is recovered after 20 s."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the equilibrium throttle setting for the desired speed\n",
    "X0, U0, Y0 = ct.find_eqpt(\n",
    "    cruise_pi, [vref[0], 0], [vref[0], gear[0], theta0[0]],\n",
    "    y0=[0, vref[0]], iu=[1, 2], iy=[1], return_outputs=True)\n",
    "\n",
    "# Now simulate the effect of a hill at t = 5 seconds\n",
    "plt.figure()\n",
    "plt.suptitle('Car with cruise control encountering sloping road')\n",
    "theta_hill = [\n",
    "    0 if t <= 5 else\n",
    "    4./180. * pi * (t-5) if t <= 6 else\n",
    "    4./180. * pi for t in T]\n",
    "t, y = ct.input_output_response(\n",
    "    cruise_pi, T, [vref, gear, theta_hill], X0)\n",
    "cruise_plot(cruise_pi, t, y, t_hill=5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of Windup\n",
    "\n",
    "The windup effect occurs when a car encounters a hill that is so steep ($6^\\circ$) that the throttle saturates when the cruise controller attempts to maintain speed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.suptitle('Cruise control with integrator windup')\n",
    "T = np.linspace(0, 50, 101)\n",
    "vref = 20 * np.ones(T.shape)\n",
    "theta_hill = [\n",
    "    0 if t <= 5 else\n",
    "    6./180. * pi * (t-5) if t <= 6 else\n",
    "    6./180. * pi for t in T]\n",
    "t, y = ct.input_output_response(\n",
    "    cruise_pi, T, [vref, gear, theta_hill], X0,\n",
    "    params={'kaw':0})\n",
    "cruise_plot(cruise_pi, t, y, label='Commanded', t_hill=5, \n",
    "            antiwindup=True, legend=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PI controller with anti-windup compensation\n",
    "\n",
    "Anti-windup can be applied to the system to improve the response. Because of the feedback from the actuator model, the output of the integrator is quickly reset to a value such that the controller output is at the saturation limit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.suptitle('Cruise control with integrator anti-windup protection')\n",
    "t, y = ct.input_output_response(\n",
    "    cruise_pi, T, [vref, gear, theta_hill], X0,\n",
    "    params={'kaw':2.})\n",
    "cruise_plot(cruise_pi, t, y, label='Commanded', t_hill=5, \n",
    "            antiwindup=True, legend=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
